Linear Regression Analysis

Introduction

This is the course reader for POL 682. The reader provides a comprehensive overview of linear regression techniques, including simple and multiple linear regression, with practical examples and visualizations.

Overview

Linear regression is a fundamental statistical technique used to model the relationship between a dependent variable and one or more independent variables. This book covers:

• Basic concepts of linear regression
• Simple linear regression
• Deriving the OLS Estimator
• Gauss-Markov Assumptions and Theorem
• Multiple linear regression
• Model diagnostics and validation
• Numerous applications with real data

Prerequisites

To follow along with the examples in this book, you should have:

• Basic knowledge of statistics
• Completed POL 681 or equivalent
• Basic understanding of R programming
• Understanding of mathematical notation
• Familiarity with matrix algebra is helpful but not required (there is also a chapter in this reader)

Structure

The book is organized into several chapters:

1. Simple Linear Regression: Introduction to modeling relationships between two variables
2. Ordinary Least Squares: Deriving the OLS estimator
3. Model Diagnostics: Checking assumptions and validating models
4. Applications and Case Studies: Practical examples with real data